I agree with the sentiment and the need for a decent way to manage the different setups for different modes but i dont agree with your artifacts or pets point.
Asking for 20 slots per artifact and pet would be a huge change and should not happen imo. A full team of heroes on goblet or garuda with 6 aviars or yulephants etc would be too much. It wouldn't fully solve the problem either as the same hero will use different artifacts and pets for different modes
What I would like to see is something which allows me to save a setup for each while choosing which of my CRests, Artifacts & Pets to apply.
Then when I play the mode my quick setup will be used which would temporarily move things around just for that mode. So we can keep the same number of artifacts and pets while enjoying the benefits of saved setups.
It also means you can have the same heroes with different crests/artifacts/pets in different modes without having to switch them manually.